Polygons

Polygons

Polygons

Polygons

Polygons

Polygons

Finally the foundation is laid to begin to look at some of the basic shapes that
characterize geometry. Most of the familiar shapes, such as squares,
triangles, rectangles, are part of a larger subset of shapes called
polygons. Polygons are geometric figures that consist of the union of
segments attached at their endpoints, ending
at the point at which they started, and not
intersecting each other. This definition is messy, but after seeing some
polygons, it will be much easier to understand. Basically, polygons have
straight sides and enclose a region in the
plane. Because they are defined in fairly
specific terms, polygons are governed by useful sets of rules that allow us, the
geometry scholars of the world, to infer things about them that aren't stated in
the problems that confront us. These special properties come in handy later on
when we'll try to prove things geometrically.

Polygons can be classified according to the number of sides they have, their
interior angles, the length of their sides,
or all three. For example, A four-sided polygon whose
angles and sides are all
congruent is a square. After laying out the
general rules of polygons, we'll take a brief look at some important types of
polygons. Quadrilaterals are classified by the relationships that exist
between their sides. Special quadrilaterals like parallelograms and
trapezoids have properties that make it easy to analyze any quadrilateral.
Another even more important polygon is the triangle. A triangle is especially
useful in the real world because by themselves triangles are simple, but they
can be united to compose any polygon in the world. With a foundation of
knowledge about triangles on the individual level, there is no limit to what
information you can extract about a shape simply by dividing it into multiple
triangles. Before we get ahead of ourselves, though, we have to understand
exactly how a point or a line
becomes a
recognizable shape.